In space, multiple unique environmental factors, particularly microgravity and space radiation, pose constant threat to the DNA integrity of living organisms. Specifically, space radiation can cause damage to DNA directly, through the interaction of charged particles with the DNA molecules themselves, or indirectly through the production of free radicals. Although organisms have evolved strategies on Earth to confront such damage, space environmental conditions, especially microgravity, can impact DNA repair resulting in accumulation of severe DNA lesions. Ultimately these lesions, namely double strand breaks, chromosome aberrations, micronucleus formation, or mutations, can increase the risk for adverse health effects, such as cancer. How spaceflight factors affect DNA damage and the DNA damage response has been investigated since the early days of the human space program. Over the years, these experiments have been conducted either in space or using ground-based analogs. This review summarizes the evidence for DNA damage induction by space radiation and/or microgravity as well as spaceflight-related impacts on the DNA damage response. The review also discusses the conflicting results from studies aimed at addressing the question of potential synergies between microgravity and radiation with regard to DNA damage and cellular repair processes. We conclude that further experiments need to be performed in the true space environment in order to address this critical question.